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UMass Lowell Computer Science 91.404 Analysis of Algorithms Prof. Karen Daniels Fall, 2009 Lecture 1 Introduction/Overview Text: Chapters 1, 2 Th. 9/3/2009

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Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_404.html

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Nature of the Course ä Core course: required for all CS majors ä Advanced undergraduate level ä Graduate students take separate course (91.503) ä No programming required ä “Pencil-and-paper” exercises ä Lectures supplemented by: ä Programs ä Real-world examples

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What’s It All About? ä Algorithm: ä steps for the computer to follow to solve a problem ä well-defined computational procedure that transforms input into output ä Some of our goals: ä recognize structure of some common problems ä understand important characteristics of algorithms to solve common problems ä select appropriate algorithm to solve a problem ä tailor existing algorithms ä create new algorithms

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Some Algorithm Application Areas Computer Graphics Robotics Bioinformatics Medical Imaging Telecommunications Design Apply Analyze

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Some Typical Problems Sorting Input: Set of items Problem: Arrange items “in order” Median finding Input: Set of numbers or keys Problem: Find item smaller than half of items and bigger than half of items SOURCE: Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at ) (for problem descriptions, see graphics gallery at http://www.cs.sunysb.edu/~algorith) Minimum Spanning Tree Input: Graph G = (V,E) with weighted edges Problem: Find subset of E of G of minimum weight which forms a tree on V Shortest Path Input: Edge-weighted graph G, with start vertex s and end vertex t Problem: Find the shortest path from s to t in G

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Tools of the Trade ä Algorithm Design Patterns such as: ä divide-and-conquer ä Data Structures such as: ä trees, linked lists, hash tables, graphs ä Algorithm Analysis Techniques such as: ä asymptotic analysis ä probabilistic analysis Growth of Functions Summations Recurrences Sets Probability MATH Proofs Logarithms Permutations Combinations

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Tools of the Trade: (continued) Algorithm Animation Formerly http://www.cs.brockport.edu/cs/java/apps/sorters/insertsortaniminp.html

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What are we measuring? ä Some Analysis Criteria: ä Scope ä The problem itself? ä A particular algorithm that solves the problem? ä “Dimension” ä Time Complexity? Space Complexity? ä Type of Bound ä Upper? Lower? Both? ä Type of Input ä Best-Case? Average-Case? Worst-Case? ä Type of Implementation ä Choice of Data Structure

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Prerequisites ä Computing I (91.101) ä Computing II (91.102) ä Discrete Math I & II (92.321, 92.322) ä Statistics for Scientists and Engineers (92.386) ä Calculus I-II (92.131-132) Growth of Functions Summations Recurrences Sets Probability MATH Proofs Logarithms Permutations Combinations

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Course Structure: 5 Parts ä Foundations ä Analyzing & Designing Algorithms, Growth of Functions, Recurrences, Probability & Randomized Algorithms ä Sorting ä Heapsort, Priority Queues, Quicksort, Sorting in Linear Time ä Data Structures ä Stacks and Queues, Linked Lists, Introduction to Trees, Hash Tables, Binary Search Trees, Balancing Trees: Red- Black Trees ä Advanced Techniques ä Dynamic Programming, Greedy Algorithms ä Graph Algorithms ä DFS, BFS, Topological Sort, MST, Shortest paths

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Textbook - - Required: ä Introduction to Algorithms ä by T.H. Corman, C.E. Leiserson, R.L. Rivest ä McGraw-Hill ä 2001 ä ISBN 0-07-013151-1 ä see course web site (MiscDocuments) for errata (1 st edition) Ordered for UML bookstore 2001 Edition

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Syllabus (current plan) Revised for Fall, 2001 in accordance with ACM Computer Science Computing Curricula 2001, Steelman Draft, August, 2001.

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CS Theory Math Review Sheet The Most Relevant Parts... ä p. 1 O, , definitions ä Series ä Combinations ä p. 2 Recurrences & Master Method ä p. 3 ä Probability ä Factorial ä Logs ä Stirling’s approx ä p. 4 Matrices ä p. 5 Graph Theory ä p. 6 Calculus ä Product, Quotient rules ä Integration, Differentiation ä Logs ä p. 8 Finite Calculus ä p. 9 Series Math fact sheet (courtesy of Prof. Costello) is on our web site.

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Important Dates ä Math Quiz (closed book) Tuesday, 9/8 ä Midterm Exam : Thursday, 10/22 ä Midterm Exam (Chapters 1-6) : Thursday, 10/22 ä Final Exam:TBA

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Grading ä ä Homework35% ä ä Midterm ( chapters 1-6, open book & notes ) 30% ä ä Discretionary ( attendance, participation, math quiz ) 5% ä ä Final Exam ( cumulative, open book & notes ) 30%

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